The repeated lives approach compares alternatives with different lifespans by repeating each alternative’s cash-flow pattern until both span the least common multiple (LCM) of their lifespans, then comparing PWs over the common horizon.
For example, alternative A has a 4-year life and alternative B has a 6-year life. LCM(4, 6) = 12. Repeat A’s cash flows three times (years 1-4, 5-8, 9-12) and B’s twice (years 1-6, 7-12), then compute the PW of each 12-year stream. The comparison is now apples-to-apples.
The mechanic is straightforward but only works under a strong assumption: each repetition of the alternative has the same cash flows as the original. The defender after one full life is replaced by an identical defender, at the same initial cost, with the same operating profile. This is a reasonable approximation for short-lived assets like software, electronics, or office equipment where successive generations are similar. For long-lived assets (decades), it’s a stretch — the world changes too much.
A clean alternative is the AW method, which side-steps lifespan-matching entirely by converting each alternative to its own per-year equivalent and comparing those directly. AW comparisons make the same implicit assumption (that future replacements have similar economics) but the assumption is buried rather than enacted.
A third option is the study period approach: pick a fixed horizon (e.g., 10 years) regardless of either alternative’s natural life; truncate longer alternatives at the horizon with a salvage value; compare PW over that horizon. This works best when the firm has a known planning horizon and isn’t actually committing to indefinite operation.
In practice: for replacement decisions and infrastructure planning, prefer AW; for one-time projects with known horizons, prefer study-period; reach for repeated-lives only when the LCM is small (≤ 30 years or so) and the repetition assumption is genuinely defensible.
See Annual worth method, Study period approach, and Comparison of alternatives for related techniques.